THE politics of the great American cities are ever the politics of ethnic succession and recombination. As the focal points for the great waves of immigration, foreign and domestic, that continually reshape the nation, it’s our cities where races historically collide, and coalesce.

Today, when we think of Fiorello La Guardia sweeping to power in New York’s 1933 mayoral contest, with his inimitable municipal version of the New Deal, we see his victory as an unalloyed progressive triumph. True enough, his victory was a backlash against the rule of Tammany Democrats, but only some La Guardia voters rejected Tammany because it was a machine.

More rejected it because it was a disproportionately Irish machine that failed to put many Italians and Jews on the city payroll. La Guardia was the good-government candidate par excellence, but, fluent in both Italian and Yiddish, he also forged a coalition of New York’s newer immigrants, its ethnic outs.

For the past quarter-century, America’s cities have been remade by our third great wave of immigration, this one predominantly from Mexico and Central America. But not until Tuesday, when Antonio Villaraigosa ousted incumbent Jim Hahn by a stunning 17-point margin to become mayor of Los Angeles, did a Latino politician put together a majority coalition in a mega-city where Latinos are a sizable bloc — but nowhere near sizable enough to elect a mayor by themselves.

In the 2000 Census, Latinos constituted fully 47 percent of L.A. residents, but so many of them were noncitizens or new citizens that as recently as the late’90s, they amounted to just 15 percent of the electorate.

By Tuesday, that figure had grown to 25 percent — a big increase, but hardly big enough to elect any but a gifted coalition builder, which Villaraigosa — fluent in Spanish, with a smattering of Yiddish — most assuredly is. For all his charisma and feel for urban complexity, however, he came up short four years ago in his first race against Hahn for mayor.

He was unable to square a circle — to construct a left-to-center majority with virtually no support from the city’s African-American community. One problem was that Hahn, who’s white, was the surrogate black candidate for reasons chiefly of genetics: His father was the legendary Kenny Hahn, who for 40 years as a county supervisor had been a pioneering advocate of civil rights. Villaraigosa’s other problem was dicier still: the racial tensions between the black and Latino communities.

Some of those tensions were grounded in economic conflicts. In the mid-’80s, for instance, Los Angeles had a heavily black unionized janitorial work force in its high-rises, until the building owners replaced them with refugees from Central America’s civil wars and Mexico’s debt crisis, at a 60 percent cut in pay. Other tensions were more directly political, as districts with long-standing black majorities turned majority-Latino between the mid-’80s and late’90s.

It should have come as no surprise, then, when L.A.’s African-American voters narrowly supported Pete Wilson’s Proposition 187 in 1994, which would have curtailed public services to undocumented immigrants had the courts not struck it down. Nor that black voters backed Hahn over Villaraigosa in 2001 by an 80 percent to 20 percent margin.

But like La Guardia, Villaraigosa is a pol for a polyglot city. From his teens, when he helped form the Black Student Union at his overwhelmingly Latino high school, to his years working the African-American community as a union staffer, he’s been the very model of the anti-nationalist urbanite.

The causes he championed while speaker of the California Assembly — massive school and parks bond measures, workers’ rights — were broad and rooted more in the calculus of class than race.

Accordingly, when Hahn stumbled in the black community — on the most parochial of issues, his well-grounded refusal to renew the contract of Bernard Parks, the city’s African-American police chief — Villaraigosa was there to pick up the pieces.

On Tuesday, according to the Los Angeles Times exit poll, he won 48 percent of the black vote (not to mention 84 percent of the Latino vote and 50 percent of the white). He carried every quadrant of this famously fractious city.

Villaraigosa’s victory will not magically dispel the city’s racial rifts, the ethnic gang rivalries, the fights at local high schools. It will not narrow the vast economic inequality that plagues contemporary U.S. cities, though Villaraigosa has supported linking development to living-wage jobs.

But the coalition he’s composed, the record he’s amassed, and the charisma and energy he’s so abundantly displayed now make Los Angeles ground zero for liberal innovation at a time of right-wing domination nearly every place else.

It’s a star turn that’s new not just for Villaraigosa, but also for the city he has now so adeptly reassembled as a showcase for urban progressivism.

Harold Meyerson is editor-at-large of American Prospect and political editor of the L.A. Weekly.